A particle moving along the x-axis is at position x = 6 when t = 0. If

where is the particle when t = 5?

The problem gives us s(0) = 6 and the value of the integral and asks for s(5). We know

so we plug in the value of the integral and the value of s(0) to get

10 = s(5) – 6.

Solving, we get

s(5) = 10 + 6 = 16.

We know the particle starts at x = 6 and moves a distance of 10 from time 0 to time 5. This means the particle must end up at position x = 16 at time t = 5.